Abstract

A model is introduced that facilitates an easy scheme to design planar multilayered waveguides. The basis of this model is a field related vector that follows simply shaped trajectories as a function of the depth coordinate in the waveguide. Its diagram provides qualitative insight into the effects upon guided modes of a change in the number of layers, in their phase thicknesses and in the state of polarization. In addition, the method offers the possibility of studying the corresponding effects upon field components inside the waveguide.

The formulas obtained in this way are comparable with Eq. (7) of Y.-F. Li and J. W. Y. Lit [6]; ϕj equals their hjdj in layers where nj > β; ψj,+ equals their −ϕj+1, but their ϕj+1 is limited to the interval [0,π) while our |ψj,+| may amount to many times 2π.

The formulas obtained in this way are comparable with Eq. (7) of Y.-F. Li and J. W. Y. Lit [6]; ϕj equals their hjdj in layers where nj > β; ψj,+ equals their −ϕj+1, but their ϕj+1 is limited to the interval [0,π) while our |ψj,+| may amount to many times 2π.

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